308 THE WORLD MACHINE 



has been observed, new facts come to light, our instant question 

 is : Do fact and theory hang together ? If not, then, as it were, 

 the theory hangs alone. But if they do if, moreover, the 

 new facts be such that they might have been more or less cal- 

 culated or divined from the previous arrangement we have a 

 feeling of certitude which nothing else can bring. When Bode 

 opened Piazzi's letter his mind instantly leaped to the idea 

 that here was the missing link of his system. 



But by that time the object, whatever it was, had disap- 

 peared from view ; he could not find it. Could its position be 

 calculated ? Mathematicians tried hard ; but the observations 

 which Piazzi had been able to make were few in number, and 

 very close one to the other. The difficulty resulted in the dis- 

 covery of a mathematician of the first order, one of the greatest 

 since Laplace. 



There was at that time in Germany a young private tutor 

 who had invented several new methods of analysis, among 

 others that which now bears the name of the " method of least 

 squares." By the aid of the latter he was able not merely to 

 construct the orbit of the new planet, for such he found it to 

 be, but to indicate to the astronomers the point where later 

 on it would be found. Just a year after Piazzi first had sight 

 of it, it was sighted again, close by where the young Gauss 

 had predicted. It was Piazzi's obvious right to name it, and 

 he called it after Sicily's protecting goddess, Ceres. 



What Bode had surmised turned out to be true ; it lay 

 between Mars and Jupiter. As calculated by Gauss, its dis- 

 tance from the sun was 2.7 times, that of the earth. In the 

 system of Bode it should have been 2.8. The agreement was 

 remarkable, but the planet was disappointing. As best it was 

 clearly only a few hundred miles in diameter ; it was smaller 

 than any heavenly body known at that time. It revolved like 

 the other planets ; but its orbit was extremely eccentric, and 

 it was tipped up ten degrees to the ecliptic, a greater amount 

 than that of any other planet then known. Altogether it was 

 a puzzle. 



The puzzle deepened when, a few months after, another 

 German astronomer, Olbers, found a second. Gauss again cal- 

 culated its path. It was found to be at almost the same distance 

 from the sun as Ceres, revolving in a yet more eccentric orbit 

 and tilted to the ecliptic at thirty-four degrees. Its bulk was 



